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Standard VIII

Mathematics

Exterior and Interior Points to an Angle

In the adjoin...

Question

In the adjoining figure, $A B C D$ is a quadrilateral such that $∠ D + ∠ C = 100^{o}$ . The bisectors of $∠ A$ and $∠ B$ meet at $∠ P$ . Determine $∠ A P B$ .

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Solution

$\begin{matrix} ∠ A + ∠ B + ∠ C + ∠ D = 360^{0} (p r o p e r t y o f Q u a d r i l a t e r a l) ∠ A + ∠ B + 100 = 360^{0} 2 ∠ P A B + 2 ∠ P B A = 260^{0} ∠ P A B + ∠ P B A = 130^{0} i n Δ A B P ∠ P A B + ∠ P B A + ∠ A P B = 180^{0} 130 + ∠ A P B = 180^{0} ∠ A P B = 180^{0} - 130^{0} = 50^{0} \end{matrix}$

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Similar questions

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In the adjoining figure, ABCD is a quadrilateral such that ∠D+∠C=100o. The bisectors of ∠A and ∠B meet at ∠P. Determine ∠APB.

∠A+∠B+∠C+∠D=3600(propertyofQuadrilateral)∠A+∠B+100=36002∠PAB+2∠PBA=2600∠PAB+∠PBA=1300inΔABP∠PAB+∠PBA+∠APB=1800130+∠APB=1800∠APB=1800−1300=500

In the adjoining figure, $A B C D$ is a quadrilateral such that $∠ D + ∠ C = 100^{o}$ . The bisectors of $∠ A$ and $∠ B$ meet at $∠ P$ . Determine $∠ A P B$ .